Our company is very interested in the Adobe software, especially in Adobe Premiere, but we still have one thing to check before we're going to buy it, most likely.

Our video editing will also be a lot about editing songs and such, now we have made a standard for the things what should be in the video. One of those things is a music frequency meter (like you in Windows Media Player). We want to enable this into the video, is this possible using Adobe Premiere? And if possible, is there a concrete tutorial for it?

For what you describe, I would strongly recommend that you look closely at two other Adobe programs: Premiere Pro and Audition. Combined, you will have infinite control, and also display capabilities, for both the Audio and the Video. Each program comes with a set of scopes that can display in RT all of the factors in the stream. PrPro in most of the "suites" ships with Soundbooth, which is a nice little audio-editor, but Audition is Soundbooth on major steroids. I use those two for 99% of my work, and love the control.

They are not priced competitively to PrE, but that is because both are true "pro" programs. With all that control comes a price tag. PrE is a great little NLE and has some audio capabilities, but for professional work, they fall far short. To try and make it work in your application would cost more in time and frustration, than the price differential.